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Math Help - 1,1,1,1 Matrix general formula!!!

  1. #16
    Newbie daRitz's Avatar
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    hmm are you sure?

    when i did (X+Y)^2, i got
    l4 0l
    l0 4l

    and i thought maybe A^n would be something like
    l2^n-1 0l
    l0 2^n-1l

    that would work for all constants right?
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  2. #17
    Lord of certain Rings
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    Quote Originally Posted by daRitz View Post
    hmm are you sure?

    when i did (X+Y)^2, i got
    l4 0l
    l0 4l
    No.You have computed it wrongly then
    First of all, X+Y = I
    And I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

    Try computing I^n and tell me what you get...


    Quote Originally Posted by daRitz View Post
    and i thought maybe A^n would be something like
    l2^n-1 0l
    l0 2^n-1l

    that would work for all constants right?
     A = aX = \begin{pmatrix} a & a \\ a & a \end{pmatrix}
    Try computing A^2, A^3 and see....
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  3. #18
    Newbie daRitz's Avatar
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    Ok thanks i understand that one now!

    Back to that previous problem,
    A=aX, B=bX
    you're formula was really good but i dont think that's what is supposed to be done because i didn't type the whole instructions:

    Let A=aX and B=bX, where a and b are constants. use different velues of a and b to calculate A^2, A^3, A^4....(for references)

    By considering integer powers of A and B, find expressions for A^n and B^n.

    i honestly have no idea what they're asking in this problem, any idea?
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  4. #19
    Lord of certain Rings
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    Quote Originally Posted by daRitz View Post

    Let A=aX and B=bX, where a and b are constants. use different velues of a and b to calculate A^2, A^3, A^4....(for references)

    By considering integer powers of A and B, find expressions for A^n and B^n.

    i honestly have no idea what they're asking in this problem, any idea?

    "use different velues of a and b to calculate A^2, A^3, A^4....(for references)"

    I am not sure what this means...

    Probably your teacher wants you to guess the general formula for A^n = (aX)^n, by first trying some values.
    Like you can try a=1, a=0 and a=2 and so on....

    This will let you see a general pattern.... Then you guess that for a particular "a",

    A^n = \begin{pmatrix} a^n2^{n-1} & a^n2^{n-1} \\ a^n2^{n-1} & a^n2^{n-1} \end{pmatrix}

    Finally you should prove this guess using induction.......
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  5. #20
    Newbie daRitz's Avatar
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    ok, well tomorrow i'll ask her before class just to be sure this is what she wants.
    thanks sooo much for your help!
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  6. #21
    Lord of certain Rings
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    Quote Originally Posted by daRitz View Post
    ok, well tomorrow i'll ask her before class just to be sure this is what she wants.
    thanks sooo much for your help!
    You are welcome
    Do tell me tomorrow what she wanted. I am curious about it
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